What is the shape of the path followed by a projectile?

According to Newton's law of gravitation,every particle of matter attracts every other particle. But bodies on the surface of the Earth never move towards each other on account of this force of attraction. Why?

Suppose the gravity of the $Earth$ suddenly becomes zero,then in which direction will the $Moon$ begin to move if no other celestial body affects it?

$A$ body weighs $63 \, N$ on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth (in $, N$)? (Given: Mass of the earth $= 6 \times 10^{24} \, kg$ and radius of the earth $= 6.4 \times 10^{6} \, m$)

$(a)$ What do you mean by free fall?
$(b)$ What happens to the direction of motion of objects during free fall?
$(c)$ $A$ stone is dropped from a height of $19.6 \, m$. Calculate:
$(i)$ Time taken to fall.
$(ii)$ How fast does it move at the end of this fall?
$(iii)$ Acceleration after $1 \, s$.

Suppose a planet exists whose mass and radius both are half that of Earth. Calculate the acceleration due to gravity on the surface of this planet.